Study Guide and Intervention (continued) - MathnMind

8-4 6-4
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Study Guide and Intervention
Polynomials
Degree of a Polynomial A polynomial is a monomial or a sum of monomials. A
binomial is the sum of two monomials, and a trinomial is the sum of three monomials.
Polynomials with more than three terms have no special name. The degree of a monomial
is the sum of the exponents of all its variables. The degree of the polynomial is the same
as the degree of the monomial term with the highest degree.
Example
State whether each expression is a polynomial. If the expression is
a polynomial, identify it as a monomial, binomial, or trinomial. Then give the
degree of the polynomial.
Expression Polynomial?
3x 7xyz
Yes. 3x 7xyz 3x (7xyz),
which is the sum of two monomials
Monomial, Binomial, Degree of the
or Trinomial? Polynomial
binomial 3
25 Yes. 25 is a real number. monomial 0
7n 3 3n 4
No. 3n4 3
, which is not
n4 a monomial
none of these —
Yes. The expression simplifies to
9x 3 4x x 4 2x 9x 3 7x 4, which is the sum trinomial 3
of three monomials
Exercises
State whether each expression is a polynomial. If the expression is a polynomial,
identify it as a monomial, binomial, or trinomial.
3
1. 36 2. 5
q2 3. 7x x 5 4. 8g 2 h 7gh 2
5. 5y 8 6. 6x x2 1
4y2 Find the degree of each polynomial.
7. 4x 2 y 3 z 8. 2abc 9. 15m
10. s 5t 11. 22 12. 18x 2 4yz 10y
13. x 4 6x 2 2x 3 10 14. 2x 3 y 2 4xy 3 15. 2r 8 s 4 7r 2 s 4r 7 s 6
16. 9x 2 yz 8 17. 8b bc 5 18. 4x 4 y 8zx 2 2x 5
19. 4x 2 1 20. 9abc bc d 5 21. h 3 m 6h 4 m 2 7
© Glencoe/McGraw-Hill 473 Glencoe Algebra 1
Lesson 8-4